Analysis of discrete-time queue with two heterogeneous servers subject to catastrophes

This paper studies a discrete-time queueing system with two heterogeneous servers subject to catastrophes. We obtain explicit expressions for the steady-state probabilities at arbitrary epoch using displacement operator method. The waiting time distribution and outside observer’s observation epoch probabilities are deduced. Various performance measures and numerical results have been investigated.Publisher's Versio

A transient solution to the M/M/c queuing model equation with balking and catastrophes

In this paper, we consider a Markovian multi-server queuing system with balking and catastrophes. The probability generating function technique along with the Bessel function properites is used to obtain a transient solution to the queuing model. The transient probabilities for the number of customers in the system are obtained explicitly. The expressions for the time-dependent expected number of customers in the system are also obtained. Finally, applications of the model are also discussed

A queueing system with batch renewal input and negative arrivals

This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process, and joins the queue/server for service. The negative arrivals are characterized by two independent Poisson arrival processes, a negative customer which removes the positive customer undergoing service, if any, and a disaster which makes the system empty by simultaneously removing all the positive customers present in the system. Using the supplementary variable technique and difference equation method we obtain explicit formulae for the steady-state distribution of the number of positive customers in the system at pre-arrival and arbitrary epochs. Moreover, we discuss the results of some special models with or without negative arrivals along with their stability conditions. The results obtained throughout the analysis are computationally tractable as illustrated by few numerical examples. Furthermore, we discuss the impact of the negative arrivals on the performance of the system by means of some graphical representations.Comment: 12 pages, 5 Figures, conferenc

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Product-form in G-networks

The introduction of the class of queueing networks called G-networks by Gelenbe has been a breakthrough in the field of stochastic modeling since it has largely expanded the class of models which are analytically or numerically tractable. From a theoretical point of view, the introduction of the G-networks has lead to very important considerations: first, a product-form queueing network may have non-linear traffic equations; secondly, we can have a product-form equilibrium distribution even if the customer routing is defined in such a way that more than two queues can change their states at the same time epoch. In this work, we review some of the classes of product-forms introduced for the analysis of the G-networks with special attention to these two aspects. We propose a methodology that, coherently with the product-form result, allows for a modular analysis of the G-queues to derive the equilibrium distribution of the network

ASIP tandem queues with consumption

The Asymmetric Inclusion Process (ASIP) tandem queue is a model of stations in series with a gate after each station. At a gate opening, all customers in that station instantaneously move to the next station unidirectionally. In our study, we enhance the ASIP model by introducing the capability for individual customers to independently move from one station to the next, and by allowing both individual customers and batches of customers from any station to exit the system. The model is inspired by the process by which macromolecules are transported within cells. We present a comprehensive analysis of various aspects of the queue length in the ASIP tandem model. Specifically, we provide an exact analysis of queue length moments and correlations and, under certain circumstances, of the queue length distribution. Furthermore, we propose an approximation for the joint queue length distribution. This approximation is derived using three different approaches, one of which employs the concept of the replica mean-field limit. Among other results, our analysis offers insight into the extent to which nutrients can support the survival of a cell.</p